{
  "id": "2209.11918",
  "version": "v1",
  "published": "2022-09-24T03:57:45.000Z",
  "updated": "2022-09-24T03:57:45.000Z",
  "title": "On the value-distribution of the logarithms of symmetric power L-functions in the level aspect",
  "authors": [
    "Philippe Lebacque",
    "Kohji Matsumoto",
    "Masahiro Mine",
    "Yumiko Umegaki"
  ],
  "comment": "56pages. arXiv admin note: substantial text overlap with arXiv:2205.00601",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider the value distribution of logarithms of symmetric power L-functions associated with newforms of even weight and prime power level. In the symmetric square case, under certain plausible analytical conditions, we prove that certain averages of those values in the level aspect, involving continuous bounded or Riemann integrable test functions, can be written as integrals involving a density function (the \"M-function\") which is related with the Sato-Tate measure. Moreover, even in the case of general symmetric power L-functions, we show the same type of formula when for some special type of test functions. We see that a kind of parity phenomenon of the density function exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-24T03:57:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11F41",
      "11M41"
    ],
    "keywords": [
      "level aspect",
      "logarithms",
      "value-distribution",
      "general symmetric power l-functions",
      "density function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}